Finite Group Databasebeta

← #15832207

Subgroups — #15832207

Order 3328.

616 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123957C212yesmaximal
2C8×#6127C211yesmaximal, characteristic
3#13113624C212yesmaximal, complemented
4#13113620C214yesmaximal, complemented
5#13113596C212yesmaximal, complemented
6#13113592C211yesmaximal, characteristic, complemented
7D13×#334C212yesmaximal, complemented
8C13×#1564C211yesmaximal, characteristic, complemented
9C4×#6127C2211yescharacteristic
10C13×#431C2212yes—
11C2×C4×C8×C13C2211yescharacteristic
12C8×C22⋊D13C412yes—
13C8×C22⋊D13C412yes—
14#11718586C2211yescharacteristic
15#11718585C2212yes—
16#11718496C2214yes—
17D13×C4⋊C8C2214yes—
18#11718389—24no—
19C8×D52—22no—
20C8×D52C411yescharacteristic
21C8×D52C411yescharacteristic
22#11718346C2212yes—
23C4×C8×D13C2212yes—
24#11718340—22no—
25C8×Dic26C411yescharacteristic
26C8×Dic26C411yescharacteristic
27C13×#335C2212yes—
28C13×#334C2211yescharacteristic
29C13×#334C2211yescharacteristic
30#11718072C2214yes—
31#11718071C2214yes—
32#11718049C2212yes—
33#11718049C2212yes—
34C2×#6127Q811yescharacteristic
35C22×C8×C13C2×C411yescharacteristic
36C22×C8×C13C2×C411yescharacteristic
37C2×C42×C13C2311yescharacteristic
38C4×C22⋊D13C2×C412yes—
39C4×C22⋊D13D412yes—
40#88180Q811yescharacteristic
41C2×#6099—22no—
42C2×C8×D13—24no—
43C2×C8×D13C2×C412yes—
44C2×C8×D13C2×C412yes—
45C4×D52C2×C411yescharacteristic
46C4×D52D411yescharacteristic
47#88126Q812yes—
48C42×D13C2312yes—
49C4×Dic26C2×C411yescharacteristic
50C4×Dic26D411yescharacteristic
51C13×C4⋊C8C2312yes—
52C13×C4⋊C8C2312yes—
53C13×C22⋊C8—22no—
54C4×C8×C13—22no—
55C4×C8×C13C2×C411yescharacteristic
56C4×C8×C13C2×C411yescharacteristic
57C4×C8×C13C2311yescharacteristic
58C4×C8×C13C2311yescharacteristic
59C22⋊#1055C2×C412yes—
60#88060—24no—
61#88060C2×C412yes—
62#88060C2×C412yes—
63#88055—24no—
64#88054—24no—
65#88054C2×C412yes—
66#88054C2×C412yes—
67C8×Dic13C2×C412yes—
68C8×Dic13C2×C412yes—
69C4⋊#1055—22no—
70C4⋊#1055C2×C411yescharacteristic
71C4⋊#1055C2×C411yescharacteristic
72C4⋊#1055C2314yes—
73C4×#1055C2312yes—
74#17834—131nomaximal, Sylow
75C22×C4×C13C22×C411yescharacteristic
76C22×C4×C13C2×D411yescharacteristic
77C22×C4×C13C2×Q811yescharacteristic
78C2×C22⋊D13C4⋊C412yes—
79#6127—24no—
80C2×D52C4⋊C411yescharacteristic
81C2×C4×D13C22×C412yes—
82C2×C4×D13C2×D412yes—
83C2×C4×D13C2×Q812yes—
84C2×Dic26C4⋊C411yescharacteristic
85C2×C8×C13—22no—
86C2×C8×C13—22no—
87C2×C8×C13—22no—
88C2×C8×C13—41no—
89C2×C8×C13C22×C411yescharacteristic
90C2×C8×C13C22×C411yescharacteristic
91C2×C8×C13C22×C411yescharacteristic
92C2×C8×C13C22×C411yescharacteristic
93C42×C13C22×C411yescharacteristic
94C42×C13C2×D411yescharacteristic
95C42×C13C2×Q811yescharacteristic
96C42×C13C2411yescharacteristic
97C22⋊Dic13C4⋊C412yes—
98#6103C4⋊C412yes—
99#6103C4⋊C412yes—
100C4⋊Dic13C4⋊C411yescharacteristic
101C4⋊Dic13C4⋊C411yescharacteristic
102#6101C4⋊C412yes—
103#6101C4⋊C412yes—
104C4×Dic13C22×C412yes—
105C4×Dic13C2×D412yes—
106C4×Dic13C2×Q812yes—
107#6099—82no—
108C2×#1055—24no—
109C2×#1055C22×C412yes—
110C2×#1055C22×C412yes—
111C8×D13—24no—
112C8×D13—42no—
113C8×D13—84no—
114#2990—132no—
115C8×#41—131no—
116#1574—132no—
117#1573—134no—
118#1568—132no—
119#1566—131no—
120#1564D1311yescharacteristic, complemented
121C2×#334—132no—
122C23×C13C2×C4⋊C411yescharacteristic
123C22×D13C2×C4⋊C412yes—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—22no—
127C2×C4×C13—22no—
128C2×C4×C13C2×C4⋊C411yescharacteristic
129C2×C4×C13C2×C4⋊C411yescharacteristic
130C2×C4×C13C2×C4⋊C411yescharacteristic
131C2×C4×C13C23×C411yescharacteristic
132C2×C4×C13C22×D411yescharacteristic
133C2×C4×C13C22×Q811yescharacteristic
134C22⋊D13—24no—
135C2×Dic13C2×C4⋊C412yes—
136C2×Dic13C2×C4⋊C412yes—
137C2×Dic13C2×C4⋊C412yes—
138D52#10814yes—
139C4×D13—24no—
140C4×D13—22no—
141C4×D13—22no—
142C4×D13—24no—
143Dic26—22no—
144C8×C13—21no—
145C8×C13—21no—
146C8×C13—21no—
147C8×C13—42no—
148C8×C13—42no—
149C8×C13#13112yes—
150#1055—22no—
151#1055—22no—
152#1055—44no—
153C4×#41—131no—
154#446—262no—
155C8×Q8—131no—
156C8×Q8—131no—
157#435—264no—
158C8×D4—132no—
159C8×D4—132no—
160C8×D4—131no—
161C8×D4—131no—
162C8×D4—262no—
163#432—134no—
164#431—131no—
165#431—132no—
166#431C2×D1312yes—
167#423—132no—
168C2×C4⋊C8—134no—
169C2×C4×C8—132no—
170C2×C4×C8C2×D1311yescharacteristic
171#335—134no—
172#335C2×D1312yes—
173#334—134no—
174#334—132no—
175#334—132no—
176#334C2×D1311yescharacteristic
177#334C2×D1311yescharacteristic
178C22×C13—21no—
179C22×C13—21no—
180C22×C13—21no—
181C22×C13C22×C4⋊C411yescharacteristic
182C2×D13—22no—
183C2×D13—22no—
184C2×D13C2×#10814yes—
185C4×C13—21no—
186C4×C13—21no—
187C4×C13—21no—
188C4×C13C2×#10812yes—
189C4×C13C2×#13111yescharacteristic
190C4×C13#56811yescharacteristic
191C4×C13#57712yes—
192Dic13—22no—
193Dic13—22no—
194Dic13—22no—
195C2×#41—131no—
196C2×M16—262no—
197C22×C8—132no—
198C22×C8—132no—
199C22×C8—264no—
200C22×C8C4×D1311yescharacteristic
201C22×C8C4×D1311yescharacteristic
202C4×Q8—131no—
203C4×Q8—131no—
204C4×D4—132no—
205C4×D4—132no—
206C4×D4—131no—
207C4×D4—131no—
208#117—131no—
209#117—132no—
210C2×C42—132no—
211C2×C42C22×D1311yescharacteristic
212C4⋊C8—132no—
213C4⋊C8—132no—
214C4⋊C8—131no—
215C4⋊C8—131no—
216C4⋊C8—134no—
217C4⋊C8—264no—
218C4⋊C8—262no—
219C4⋊C8C22×D1312yes—
220C4⋊C8C22×D1312yes—
221C22⋊C8—22no—
222C22⋊C8—132no—
223C22⋊C8—132no—
224C22⋊C8—132no—
225C22⋊C8—264no—
226#97—264no—
227C4×C8—22no—
228C4×C8—132no—
229C4×C8—132no—
230C4×C8—132no—
231C4×C8C4×D1311yescharacteristic
232C4×C8C4×D1311yescharacteristic
233C4×C8C22×D1311yescharacteristic
234C4×C8C22×D1311yescharacteristic
235C2×C13—41no—
236C2×C13#290611yescharacteristic
237C2×C13#291211yescharacteristic
238C2×C13C22×#10811yescharacteristic
239D13—24no—
240#41—264no—
241C2×Q8—131no—
242C2×D4—132no—
243C2×D4—131no—
244C22×C4—132no—
245C22×C4—132no—
246C22×C4—132no—
247C22×C4C2×C4×D1311yescharacteristic
248C22×C4D4×D1311yescharacteristic
249C22×C4Q8×D1311yescharacteristic
250M16—1042no—
251C2×C8—22no—
252C2×C8—22no—
253C2×C8—22no—
254C2×C8—41no—
255C2×C8—132no—
256C2×C8—132no—
257C2×C8—264no—
258C2×C8—264no—
259C2×C8—522no—
260C2×C8—1044no—
261C2×C8C2×C4×D1311yescharacteristic
262C2×C8C2×C4×D1311yescharacteristic
263C2×C8C2×C4×D1311yescharacteristic
264C2×C8C2×C4×D1311yescharacteristic
265C4⋊C4—132no—
266C4⋊C4—132no—
267C4⋊C4—131no—
268C4⋊C4—131no—
269C22⋊C4—132no—
270C22⋊C4—132no—
271C22⋊C4—132no—
272C42—132no—
273C42—132no—
274C42—132no—
275C42C2×C4×D1311yescharacteristic
276C42D4×D1311yescharacteristic
277C42Q8×D1311yescharacteristic
278C42C23×D1311yescharacteristic
279C13#1783411yescharacteristic, complemented, Sylow
280C23—132no—
281C23C4⋊C4×D1311yescharacteristic
282Q8—262no—
283D4—134no—
284D4—264no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—132no—
290C2×C4—132no—
291C2×C4—132no—
292C2×C4—264no—
293C2×C4—262no—
294C2×C4—262no—
295C2×C4—264no—
296C2×C4C4⋊C4×D1311yescharacteristic
297C2×C4C4⋊C4×D1311yescharacteristic
298C2×C4C4⋊C4×D1311yescharacteristic
299C2×C4C22×C4×D1311yescharacteristic
300C2×C4C2×D4×D1311yescharacteristic
301C2×C4C2×Q8×D1311yescharacteristic
302C8—21no—
303C8—21no—
304C8—21no—
305C8—42no—
306C8—42no—
307C8—262no—
308C8—262no—
309C8—524no—
310C8#8815512yes—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—134no—
315C22—262no—
316C22—262no—
317C22C2×C4⋊C4×D1311yescharacteristic
318C4—21no—
319C4—21no—
320C4—21no—
321C4—262no—
322C4—262no—
323C4—262no—
324C4D13×#10812yes—
325C4C2×#8815511yescharacteristic
326C4#1171945011yescharacteristic
327C4#1171947512yes—
328C2—41no—
329C2—264no—
330C2#1312340111yescharacteristic
331C2#1312342811yescharacteristic
332C2C2×D13×#10811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1564C2
socleC22×C13C22×C4⋊C4
prime radicalC2×#6127Q8
cosocleC42×C13C24
hypercenter#1564D13
hypocenterC13#17834
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1564

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #13113624C2semidirect
4. #13113620C2semidirect
5. #13113596C2semidirect
6. #13113592C2semidirect
7. D13×#334C2semidirect
8. C13×#1564C2semidirect
120. #1564D13semidirect
279. C13#17834semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#131239572
C8×#61272
#131136242
#131136202
#131135962
#131135922
D13×#3342
C13×#15642
#1783413